Details

Time bar (total: 9.8s)

analyze661.0ms (6.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.7s (27.6%)

Results
779.0ms5427×body128valid
762.0ms1131×body2048valid
342.0ms740×body1024valid
289.0ms412×body4096valid
264.0ms1073×body128invalid
124.0ms371×body512valid
41.0ms175×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify266.0ms (2.7%)

Algorithm
egg-herbie
Rules
1743×fma-neg_binary64
1393×fma-def_binary64
800×div-sub_binary64
619×times-frac_binary64
473×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
26722
313822
420422
533822
655822
792422
8138822
9160422
10237522
11274222
12253322
13262122
14317122
15331322
16387322
17367922
18402922
19431722
20448522
21456122
22480522
23479322
24479722
25479722
26494822

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
32.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
33.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
32.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
1.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
22.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series128.0ms (1.3%)

Counts
4 → 96
Calls

4 calls:

56.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
34.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
29.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
9.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite117.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
278×expm1-udef_binary64
278×log1p-udef_binary64
166×add-sqr-sqrt_binary64
162×log1p-expm1-u_binary64
162×expm1-log1p-u_binary64
Counts
4 → 158
Calls

4 calls:

113.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
113.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
113.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
113.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01574
133762
2415862
3498762
4485062

simplify79.0ms (0.8%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
436×fma-def_binary64
432×fma-neg_binary64
426×associate-/r*_binary64
Counts
254 → 231
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
13982164
213272078
349542078
452182078

prune242.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New21912231
Fresh101
Picked101
Done000
Total22112233
Error
5.4b
Counts
233 → 12
Alt Table
StatusErrorProgram
44.8b
(*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) 2))
39.3b
(neg.f64 (/.f64 c b))
56.3b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
45.0b
(/.f64 (/.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))) (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) (*.f64 2 a))
47.3b
(-.f64 (/.f64 c b) (/.f64 b a))
44.8b
(pow.f64 (/.f64 (*.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) -1)
47.0b
(/.f64 (neg.f64 b) a)
32.9b
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
51.8b
(-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
45.0b
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))) 2) (pow.f64 (cbrt.f64 (*.f64 a 2)) 2)) (cbrt.f64 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))))
33.8b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))))) (*.f64 2 a))
48.5b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
Compiler

Compiled 6258 to 3684 computations (41.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -4 (*.f64 a c))
0.1b
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
1.2b
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b)
22.8b
(sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))

series124.0ms (1.3%)

Counts
4 → 84
Calls

4 calls:

54.0ms
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
34.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b)
32.0ms
(sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))
4.0ms
(*.f64 -4 (*.f64 a c))

rewrite87.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
328×fma-def_binary64
255×expm1-udef_binary64
255×log1p-udef_binary64
215×fma-neg_binary64
181×egg-rr
Counts
4 → 181
Calls

4 calls:

83.0ms
(*.f64 -4 (*.f64 a c))
83.0ms
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
83.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b)
83.0ms
(sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01358
128355
2370755
3492255

simplify82.0ms (0.8%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
430×fma-neg_binary64
426×associate-/r*_binary64
421×fma-def_binary64
Counts
265 → 250
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01202007
13961984
213211898
349361898
452001898

prune207.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2446250
Fresh5611
Picked011
Done000
Total24913262
Error
5.4b
Counts
262 → 13
Alt Table
StatusErrorProgram
32.7b
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)) -1)
48.5b
(/.f64 (*.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
47.3b
(-.f64 (/.f64 c b) (/.f64 b a))
34.7b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b))) (*.f64 2 a))
32.9b
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
51.8b
(-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
39.3b
(neg.f64 (/.f64 c b))
39.3b
(fma.f64 (/.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) 2) (/.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c))))) a) (neg.f64 (/.f64 b (*.f64 a 2))))
43.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))))) (*.f64 2 a))
55.1b
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) (sqrt.f64 b))) (*.f64 2 a))
33.8b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))))) (*.f64 2 a))
47.0b
(/.f64 (neg.f64 b) a)
56.3b
(/.f64 (-.f64 b b) (*.f64 2 a))
Compiler

Compiled 6547 to 3916 computations (40.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b))
0.1b
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)) -1)
0.4b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)
13.1b
(sqrt.f64 (*.f64 -4 (*.f64 a c)))

series1.4s (14.4%)

Counts
4 → 36
Calls

4 calls:

993.0ms
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)) -1)
311.0ms
(/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b))
87.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)
13.0ms
(sqrt.f64 (*.f64 -4 (*.f64 a c)))

rewrite119.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
577×prod-diff_binary64
178×egg-rr
158×add-sqr-sqrt_binary64
151×log1p-expm1-u_binary64
151×expm1-log1p-u_binary64
Counts
4 → 178
Calls

4 calls:

114.0ms
(/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b))
114.0ms
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)) -1)
114.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)
114.0ms
(sqrt.f64 (*.f64 -4 (*.f64 a c)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01569
132366
2391066
3501066

simplify67.0ms (0.7%)

Algorithm
egg-herbie
Rules
590×associate-/l*_binary64
568×associate-/r*_binary64
406×fma-def_binary64
371×fma-neg_binary64
218×associate-*r/_binary64
Counts
214 → 246
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01381518
14471376
214341333
348611333
450051333

prune311.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2442246
Fresh4711
Picked011
Done011
Total24811259
Error
1.8b
Counts
259 → 11
Alt Table
StatusErrorProgram
48.5b
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 -4 a)) (sqrt.f64 c))) b)) -1)
33.8b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))))) (*.f64 2 a))
44.8b
(pow.f64 (fma.f64 4 (/.f64 a (/.f64 (*.f64 -4 (*.f64 c a)) b)) (/.f64 a b)) -1)
32.9b
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
51.8b
(-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
39.3b
(neg.f64 (/.f64 c b))
39.3b
(fma.f64 (/.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) 2) (/.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c))))) a) (neg.f64 (/.f64 b (*.f64 a 2))))
43.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))))) (*.f64 2 a))
55.1b
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) (sqrt.f64 b))) (*.f64 2 a))
32.7b
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)) -1)
47.3b
(-.f64 (/.f64 c b) (/.f64 b a))
Compiler

Compiled 6747 to 4293 computations (36.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))
8.2b
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))))
22.8b
(sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))
23.7b
(cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))

series126.0ms (1.3%)

Counts
3 → 92
Calls

3 calls:

47.0ms
(cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))
43.0ms
(cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))
36.0ms
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))))

rewrite71.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
585×log-prod_binary64
338×fma-def_binary64
213×expm1-udef_binary64
213×log1p-udef_binary64
205×fma-neg_binary64
Counts
3 → 125
Calls

3 calls:

68.0ms
(cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))
68.0ms
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))))))
68.0ms
(cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01446
127042
2295642
3534042

simplify106.0ms (1.1%)

Algorithm
egg-herbie
Rules
299×associate-*r*_binary64
259×associate-/r*_binary64
250×times-frac_binary64
242×fma-neg_binary64
206×fma-def_binary64
Counts
217 → 251
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03654666
112214570
246884530
349664530

prune248.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New2970297
Fresh088
Picked011
Done022
Total29711308
Error
1.8b
Counts
308 → 11
Alt Table
StatusErrorProgram
48.5b
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 -4 a)) (sqrt.f64 c))) b)) -1)
33.8b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))))))) (*.f64 2 a))
44.8b
(pow.f64 (fma.f64 4 (/.f64 a (/.f64 (*.f64 -4 (*.f64 c a)) b)) (/.f64 a b)) -1)
32.9b
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) b) (*.f64 2 a))
51.8b
(-.f64 (*.f64 -2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
39.3b
(neg.f64 (/.f64 c b))
39.3b
(fma.f64 (/.f64 (cbrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c)))) 2) (/.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c))))) a) (neg.f64 (/.f64 b (*.f64 a 2))))
43.5b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) (*.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))))) (*.f64 2 a))
55.1b
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) (sqrt.f64 b)) (-.f64 (pow.f64 (fma.f64 b b (*.f64 -4 (*.f64 a c))) 1/4) (sqrt.f64 b))) (*.f64 2 a))
32.7b
(pow.f64 (/.f64 (*.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)) -1)
47.3b
(-.f64 (/.f64 c b) (/.f64 b a))
Compiler

Compiled 11951 to 7450 computations (37.7% saved)

regimes2.3s (23.8%)

Accuracy

Total 7.4b remaining (72.5%)

Threshold costs 0b (0%)

Counts
175 → 3
Compiler

Compiled 16120 to 11258 computations (30.2% saved)

bsearch85.0ms (0.9%)

Steps
ItersRangePoint
8
2.400025064915491e-90
1.0344018153467932e-87
4.4569387361564705e-88
11
-1.6271106088346776e+157
-2.3352557794860317e+135
-4.11211753122393e+143
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02550
13750
24450
34950
45150
55150

end156.0ms (1.6%)

Compiler

Compiled 322 to 213 computations (33.9% saved)

Profiling

Loading profile data...